Abstract
The definition of a new multiplier and the modification of the multi-θ method of convergence are developed for solving distillation problems. Furthermore, a procedure for stabilizing the numerical calculations and for yielding rapid solutions is proposed. It is found that an assumed value of a multiplier in each iterative computation can be assigned to an arbitrary number, and that it is better to be set equal to unity. To demonstrate the advantage of the proposed damping method, some numerical examples for distillation with hydrolysis of methyl acetate are presented. The reactive distillation problems are solved with the proposed procedure, and the results are compared with those by a conventional method. The proposed method constricts the large excursion resulting from the Newton-Raphson method. Then the corrected values can be confined within a region of convergence. The procedure proposed herein may be extended to other types of multistage separation processes.
